Acoustic noise cancellation problems arise in a number of industrial applications; in medical equipment like magnetic resonance imaging; in air ducts; in high quality headsets, headphones, handset etc., where it is required to reduce a background noise in a location of a listener. As the noise arises, propagates and exists in air, i.e. in acoustic environment, the noise can be cancelled or attenuated in acoustical way only. This problem is usually solved by Active Noise Control (ANC) systems. The ANC system produces anti-noise, i.e. acoustic wave, with the same amplitude and opposite phase as those of the cancelling noise in a plane of the cancellation. The principle of a sine wave noise 11 cancellation by anti-noise 12 is illustrated by the graph 10 shown in FIGS. 1a, 1b and 1c. 
If noise 11 and anti-noise 12 have the same amplitude and opposite phase, then a perfect cancellation of the noise is achieved as shown in FIG. 1a. If there is amplitude (see FIG. 1b) or phase (see FIG. 1c) mismatch, then a partial cancellation, i.e. attenuation, of the noise is achieved only. Here 13 is residual (cancelled or attenuated) noise. The ANC systems are the systems, which can adjust the above mismatch during operation with respect to mismatch minimization.
As the performance of an ANC system depends on its architecture and used algorithms, there is a need to improve active noise cancellation.
In order to describe the disclosure in detail, the following terms, abbreviations and notations will be used:
ANC: active noise control, active noise cancellation
AP: affine projection
DAC: digital-to-analog converter
dB: decibel(s)
FB: feed-backward
FF: feed-forward
FAP: fast AP
GASS: gradient adaptive step size
Hybrid: combination of FB and FF
LMS: least mean squares
NLMS: normalized LMS
PSD: power spectral density
RLS: recursive least squares
WGN: white Gaussian noise.